Related papers: A quantum algorithm for computing the Carmichael f…
A deterministic algorithm for factoring $n$ using $n^{1/3+o(1)}$ bit operations is presented. The algorithm tests the divisibility of $n$ by all the integers in a short interval at once, rather than integer by integer as in trial division.…
Quantum random walks on graphs have been shown to display many interesting properties, including exponentially fast hitting times when compared with their classical counterparts. However, it is still unclear how to use these novel…
Quantum Search Algorithm made a big impact by being able to solve the search problem for a set with $N$ elements using only $O(\sqrt{N})$ steps. Unfortunately, it is impossible to reduce the order of the complexity of this problem, however,…
We give the first quantum circuit for computing $f(0)$ OR $f(1)$ more reliably than is classically possible with a single evaluation of the function. OR therefore joins XOR (i.e. parity, $f(0) \oplus f(1)$) to give the full set of logical…
We have taken significant steps towards the realization of a practical quantum computer: using nuclear spins and magnetic resonance techniques at room temperature, we provided proof of principle of quantum computing in a series of…
A quantum algorithm is a set of instructions for a quantum computer, however, unlike algorithms in classical computer science their results cannot be guaranteed. A quantum system can undergo two types of operation, measurement and quantum…
Finding the maximum value of a function in a dynamic model plays an important role in many application settings, including discrete optimization in the presence of hard constraints. We present an iterative quantum algorithm for finding the…
We describe a simple quantum algorithm for preparing $K$ copies of an $N$-dimensional quantum state whose amplitudes are given by a quantum oracle. Our result extends a previous work of Grover, who showed how to prepare one copy in time…
In quantum algorithms discovered so far for simulating scattering processes in quantum field theories, state preparation is the slowest step. We present a new algorithm for preparing particle states to use in simulation of Fermionic Quantum…
Quantum algorithms require less operations than classical algorithms. The exact reason of this has not been pinpointed until now. Our explanation is that quantum algorithms know in advance 50% of the solution of the problem they will find…
This paper shows that a quantum mechanical algorithm that can query information relating to multiple items of the database, can search a database in a single query (a query is defined as any question to the database to which the database…
The partition function is an essential quantity in statistical mechanics, and its accurate computation is a key component of any statistical analysis of quantum system and phenomenon. However, for interacting many-body quantum systems, its…
We investigate the complexity of algorithms counting ones in different sets of operations. With addition and logical operations (but no shift) $O(\log^2(n))$ steps suffice to count ones. Parity can be computed with complexity $O(\log(n))$,…
The current paper presents a new quantum algorithm for finding multicollisions, often denoted by $\ell$-collisions, where an $\ell$-collision for a function is a set of $\ell$ distinct inputs that are mapped by the function to the same…
Finance is one of the promising field for industrial application of quantum computing. In particular, quantum algorithms for calculation of risk measures such as the value at risk and the conditional value at risk of a credit portfolio have…
We study quantum algorithms working on classical probability distributions. We formulate four different models for accessing a classical probability distribution on a quantum computer, which are derived from previous work on the topic, and…
This paper presents a computer program, written in Maple, that allows a user to simulate certain aspects of Shor's quantum factoring algorithm on a desktop or laptop computer. The program does not simulate the unitary operations carried out…
We propose an algebraic formulation for two distinct quantum algorithms: a quantum classification algorithm and a quantum search algorithm with a non-uniform initial distribution, both based on Clifford algebras and spinorial…
We propose a class of randomized quantum algorithms for the task of sampling from matrix functions, without the use of quantum block encodings or any other coherent oracle access to the matrix elements. As such, our use of qubits is purely…
Quantum contextuality is a limitation on deterministic hidden variable models, testable in measurement scenarios where outcomes differ under quantum or classical descriptions due to a common set of constraints. When considering measurements…